Carrier thermalization inCu2O: Phonon emission by excitons

We have observed the energy distribution of nonthermalized excitons in the semiconductor ${\mathrm{Cu}}_2$O on a time scale of 10 ps following resonant creation by a short (5-ps) laser pulse. We present a model for the change in the energy distribution of carriers as they cool to take on a Maxwell-Boltzmann distribution at the lattice temperature. Emission and absorption of acoustic phonons via the deformation-potential interaction and emission and absorption of nonpolar optical phonons are taken into account in an exact Boltzmann equation that is solved numerically. The model fits the observed distributions well, for a value of the deformation potential in agreement with hydrostatic-pressure and uniaxial-stress measurements. Single-optical-phonon emission is found to be rather slow, with a time scale of about 30 ps. We also present evidence for a fast two-optical-phonon emission process in ${\mathrm{Cu}}_2$O. Finally, we consider the effects of exciton-exciton interactions and obtain an upper bound on the range of exciton-exciton interactions from these experiments.